Semigroups of ...-density continuous functions.
Semilinear fractional order integro-differential equations with infinite delay in Banach spaces
This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.
Semilinear functional differential equations of fractional order with state-dependent delay.
Separate approximate continuity and strong approximate continuity
Separating sets by Darboux-like functions
We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).
Separation by monotonic functions.
Separation via quadratic functions.
Separation via quadratic functions. (Summary).
Series solutions of time-fractional PDEs by homotopy analysis method.
Set-valued fractional order differential equations in the space of summable functions
In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type , a.e. on (0,1), , αₙ ∈ (0,1), where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.
Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions
We make some comments on the problem of how the Henstock-Kurzweil integral extends the McShane integral for vector-valued functions from the descriptive point of view.
Sharkovskiĭ's theorem holds for some discontinuous functions
We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected graph.
Sharp error bounds for the trapezoidal rule and Simpson's rule.
Sharp estimates of the curvature of some free boundaries in two dimensions.
Sharpening of Jordan's inequality and its applications.
Sierpiński's hierarchy and locally Lipschitz functions
Let Z be an uncountable Polish space. It is a classical result that if I ⊆ ℝ is any interval (proper or not), f: I → ℝ and then f ○ g ∈ for every if and only if f is continuous on I, where stands for the αth class in Baire’s classification of Borel measurable functions. We shall prove that for the classes in Sierpiński’s classification of Borel measurable functions the analogous result holds where the condition that f is continuous is replaced by the condition that f is locally Lipschitz...
Sign changes in linear combinations of derivatives and convolutions of Polya frequency functions.
Slowly oscillating continuity.
Smooth Cantor functions
We characterise the set on which an infinitely differentiable function can be locally polynomial.
Smooth rough paths and applications to Fourier analysis.